There is a 120 L mixture of vinegar and water. The ratio of vinegar to water is 7 ∶ 5. A shopkeeper mixes a certain amount of water in order to make the ratio of vinegar to water 5 ∶ 6. The new quantity of water is what percentage of the original quantity of water in the mixture?
168%
Mixture Problem: Understanding Vinegar and Water Ratios
This problem involves a mixture of vinegar and water where the ratio changes after adding more water. We need to find out how the new quantity of water relates to the original quantity as a percentage.
Vinegar and Water: Initial Quantities
First, let's determine the initial amounts of vinegar and water in the mixture. We are given:
- Total volume of the mixture = 120 L
- Initial ratio of vinegar to water = 7 ∶ 5
To find the individual quantities, we sum the parts of the ratio:
\( \text{Total parts} = 7 \text{ (vinegar)} + 5 \text{ (water)} = 12 \text{ parts} \)
Now, we find the volume represented by one part:
\( \text{Value of 1 part} = \frac{\text{Total volume}}{\text{Total parts}} = \frac{120 \text{ L}}{12} = 10 \text{ L/part} \)
Using this, we can calculate the initial quantities:
- Initial quantity of vinegar: \( 7 \text{ parts} \times 10 \text{ L/part} = 70 \text{ L} \)
- Original quantity of water: \( 5 \text{ parts} \times 10 \text{ L/part} = 50 \text{ L} \)
Let's summarize the initial mixture composition:
| Component | Quantity (L) |
|---|---|
| Vinegar | 70 |
| Water | 50 |
| Total Mixture | 120 |
Water Added: Calculating New Quantities
A certain amount of water is added to the mixture, and the new ratio of vinegar to water becomes 5 ∶ 6. It's important to remember that the quantity of vinegar remains constant because only water is added.
- Constant quantity of vinegar = 70 L
- New ratio of vinegar to water = 5 ∶ 6
In the new ratio, the 5 parts correspond to the vinegar. So, we can find the value of one part in the new ratio:
\( 5 \text{ parts (new ratio)} = 70 \text{ L (vinegar)} \)
\( \text{Value of 1 part (new ratio)} = \frac{70 \text{ L}}{5} = 14 \text{ L/part} \)
Now, we can calculate the new quantity of water using the new ratio:
\( \text{New quantity of water} = 6 \text{ parts (new ratio)} \times 14 \text{ L/part} = 84 \text{ L} \)
Percentage Calculation: New Water vs. Original Water
The final step is to find the new quantity of water as a percentage of the original quantity of water in the mixture.
- Original quantity of water = 50 L
- New quantity of water = 84 L
To calculate the percentage, we use the formula:
\( \text{Percentage} = \left( \frac{\text{New quantity of water}}{\text{Original quantity of water}} \right) \times 100\% \)
Substituting the values:
\( \text{Percentage} = \left( \frac{84 \text{ L}}{50 \text{ L}} \right) \times 100\% \)
\( \text{Percentage} = 1.68 \times 100\% \)
\( \text{Percentage} = 168\% \)
Therefore, the new quantity of water is 168% of the original quantity of water in the mixture.
Important Questions from To Make a Mixture from Two Mixtures
- A and B are two alloys of gold and copper prepared by mixing the metals in the ratio of 7 : 2 and 7 : 11, respectively. Equal quantities of the alloys are melted to form a third alloy, C. If the amount of copper in C is 10 kg, then what is the amount of gold in C?
Two solutions A and B having sugar concentrations of 65% and 85% respectively are required to make a mixture. In what ratio these two solutions be mixed to get a mixture of sugar concentration 73%
In what ratio should cement costing Rs. 250 per bag be mixed with cement costing Rs. 325 per bag so that the cost of the mixture is Rs. 300 per bag. (A bag of cement is 50 kg).
A money lender finds that due to the fall in the annual rate of interest from 18% to 15%, his yearly income diminishes by Rs. 750. His capital is:
In what ratio must a mixture of 15% spirit strength be mixed with that of 25% spirit strength to get a mixture of 21% spirit strength?
